OP I agree with the above from JJtrying2024 and an earlier poster suggesting they collect from day care on adhoc afternoons agreed with you and day care.
You just need to stick to your guns and say at the moment that's the only way to give her more time with him, if that's what she would like to do. Perhaps she might like to choose an afternoon every so often so he can meet up with her friend and grandson!
I think you just need to say he's at regular daycare which is needed so you can work, evenings after work end up being busy with getting dinner, his evening routine and then getting him settled into bed which is not always very easy. And then when its the weekends that's really the only relaxed time you and your husband get to have with him or each other.
If she says about her friend and her friend's grandson just say well they have a completely different family situation and each child is different - your son is just more reserved, and I'd remind her that she doesn't want (and said so) the restriction of regular child care, and that you respect that and would never expect it of her. Likewise you hope she respects that you and your husband needs weekends where possible as relaxed ones with your son. I'd remind her that you are juggling time with both sets of grandparents and trying to be fair about it. So ad hoc arranged pick ups after day care are the best compromise you can think of.
I'd mention that you are very grateful for all her offers of baby sitting and that you hope to take her up on at at some point when things are easier. But at the moment you and your husband need to have your time with him. I'd point out that things may well change as he gets older, but this is the situation now.
OP I mention the above because you might feel that it would be nice for you to have a romantic evening or catch up with friends etc. Its also good for your son to have a rountine varied occasionally (maybe not now I realise but when he's older).
Don't dismiss the idea of them babysitting altogether (even if you aren't ready now). I say that as my mum wasn't well enough to babysit (although she would have loved to), and my PILs never wanted to. I could count on 1 hand how many times they babysat my 2 boys while they were growing up even during hospital emergencies (and they lived 30 mins away). They also told us when I was first pregnant not to expect them to ever have our children after school.
I don't think grandparents should be expected to be after school child care, and I've seen grandparents who were massively unfairly taken advantaged of by their entitled daughters and son in laws who never seemed to notice or care how much the grand parents were doing - which I don't agree with. But I have noticed that grandparents who do help out in some capacity often do have a closer relationship. So personally I think grand parents being involved is valuable for children and the relationship between the two. When I have grandchildren I would like to be able to help out (with boundaries all are happy with).
I also understand about the weekend you see them being taken up and that it's never for just a while. We had a similiar issue with my PILs - because they didn't see the boys that often (their choice), when we visited as a family it ended up being a formal performance that followed certain rigid routine and wasn't a relaxed informal get together. We never ended up trying to change that because in their case (unlike your mum) they weren't interested in seeing us or the boys very often.
You may not want to do this yet, but in the case with your parents, it might be worth you trying to work on making some ad hoc visits, outside of your allocated weekend with them, relaxed shorter ones so that you could pop for a coffee, then leave after say 40 mins or an hour, if for example you have to go somewhere else or your husband calls you back for lunch etc etc. Break things up abit. That way they see your son abit more regularly but you protect the majority of your weekend.
The other way might be to meet up with your parents and your PILs at the same time to do a combined activity? That might free up some weekend time.
I was SAHM until my eldest was in Primary, but when I was working afterwards I do remember how the weekends just vanished. So I do understand how precious that time with just you, your husband and your son is.